The Largest Automorphism Group of a Del Pezzo Surface of Degree \(2\) without Points

Abstract

We construct an example of a field and a smooth del Pezzo surface of degree \(2\) over this field without points such that its automorphism group is isomorphic to \(\mathrm{PSL}_2(\mathbb{F}_7) \times \mathbb{Z}/2\mathbb{Z}\), which is the largest possible automorphism group for del Pezzo surfaces of degree \(2\) over an algebraically closed field of characteristic zero.